Wavetable synthesis:

Wavetable synthesis is a technique used in certain digital music synthesizers to implement a restricted form of real-time additive synthesis. The technique was first developed by Wolfgang Palm of PPG in the late 1970s, and has since been used in various forms in other synthesizers built by Sequential Circuits, Ensoniq, Yamaha, Korg and Waldorf Music. The signature sound associated with wavetable synthesis is owed to the limitations of the technique and heavily influenced by the widely varying implementation details.

Theory of operation

The basis of wavetable synthesis are bandlimited periodic waveforms (time-domain implementation) or (mathematically equivalent) finite harmonic spectra (frequency-domain implementation). The evolution of musical timbre over time is approximated by placing different waveforms or spectra in a table and picking the most appropriate one at any time instant during playback.^[1] Since simply switching between two dissimilar waveforms can introduce unpleasant artifacts into the sound, the wavetable has to fulfill certain requirements depending on the implementation details. For instance, the wavetables are often arranged so that the start sample for each waveform is at a positive-going zero-crossing and a switch from one waveform to the other is only done at these zero-crossings. Another refinement is to (additionally)interpolate between two or more different waveforms or spectra to produce smoothly varying timbres and to reduce the storage requirements. By restricting the waveforms to be symmetrical, the storage requirements can be halved.

Unfortunately the term wavetable may have quite different meanings depending on context. The original usage as introduced by PPG was for a collection of waveforms to be put successively into memory by interpretation of a wave control table which contained pointers to ROM waves and escape characters to effect interpolation between those ROM waves. When used in the context of arbitrary waveform generation, direct digital synthesis or numerically-controlled oscillators the term wavetable refers to the samples of a single (periodic) waveform. In a frequency-domain implementation the same term may be used for the result of rendering a spectrum into the time-domain or even less accurate for the components of the spectrum itself.

Wavetable creation

To imitate the sound of an existing instrument with wavetable synthesis, a single note (with constant pitch) is sampled and processed using a spectrum analyzer, producing a graph of overtones contained in the sample. This graph is then parsed into a sequence of samples or wavetables, each having one period or cycle per table, generated by adding together the partials at each parse point.^[2] A set of wavetables with user specified harmonic content can also be generated mathematically. Both methods of producing a wavetable are easily combined. The mathematical equivalence of time-domain and frequency-domain representation also makes it possible to freely change between both during creation of a wavetable.

Editors for wavetables are not commonly available directly with the synthesizer, but often require hardware extensions like the PPG Waveterm or the use of software running on a separate computer. Even then the creation of wavetables is something most musicians find arcane and difficult as the results can be unpredictable to someone not familiar with the intricacies of the particular implementation. Recognizing this, several synthesizers have been produced that provide no or only hidden facilities to use wavetables different from the presets that come with the unit.

Practical Use

During playback, the waveform produced can be changed by switching to a different starting point in the wavetable, usually on command from an envelope generator or low frequency oscillator. Doing this modifies the spectral characteristics of the output wave in real time, producing sounds that can imitate certain analog instruments (such as organs, pianos, harpsichords and reed instruments) acceptably without requiring the use of a pulse code modulation technique, which requires much more memory and higher sample rates for good results. The technique is also useful for evolving pads, where the waveform changes slowly over time and can reverse itself or loop back to an arbitrary point.

The key to create convincing musical results on a wavetable synthesizer lies in the choice (or creation) of a suitable wavetable and the control of the playback point within that table. It is often necessary to understand how the wavetable was created to make correct use of it. Many wavetables contain the attack portion of a sound followed by sustain and release; that is the temporal evolution of the timbre is encoded into the wavetable. In other instances the wavetable contains different timbres of the same sound to be used in conjunction with different pitches during playback, which is for instance necessary for a vocal choir to keep the formants from shifting with the playback pitch. These two different techniques may even be combined into a single wavetable.

Since a wavetable oscillator can generate arbitrary waveforms, it is also possible to load simple sine wave, square wave and sawtooth wave tables and use the synthesizer like an analog synthesizer, using subtractive synthesis to modify the sound. Also, some wavetable synthesizers (such as the PPG Wave 2.3 with Waveterm) can reset the loop point on the phase accumulator to a period longer than a single cycle, making a PCM mode possible with minimal hardware changes.

Comparison with other digital synthesis techniques

Wavetable synthesis has similar capabilities to other synthesizers in the real-time additive synthesis family, as well as to digital frequency modulation synthesis systems such as the Yamaha DX and OPx series; however, wavetable synthesizers require less hardware to produce a usable system. The entire oscillator can be implemented using a few 7400 series TTL ICs and small-capacity static RAM ICs, something that was important in the late 1970s and early 1980s (when memory prices were still relatively high, and high-powered CPUs such as the Motorola 68000 were uncommon and expensive); most other digital synthesizers of the time either implemented each partial separately, making assembly more complex (this is also how most electronic organs are built), or used custom ICs to bring the chip count down.

Later wavetable synthesizers have antialiasing capabilities (where the transitions between waves are mediated by the CPU instead of simply switching the starting address of the loop) as well as subtractive-style filters (since the moving filter effect that a wavetable patch provides is somewhat "harsh" and FM-like without antialiasing, and filters were easier to implement at the time).

Confusion with sample-based synthesis

Starting around 1993, with the introduction of Creative Labs' Sound Blaster AWE32 and Gravis's Ultrasound cards, the term "wavetable" started to be applied to any sound card that had a better General MIDI subsystem than the then-common OPL2 and OPL3 FM synthesizers. This was based on a misunderstanding between the technical definition of a wavetable (which is the actual sample data used to generate an arbitrary wave), and the PPG usage of the term (which referred specifically to their implementation of wavetable synthesis, as described above). The AWE32 was not an additive synthesizer, but a high-end sampler and subtractive synthesis system based on technology from the E-mu Emulator family.

The description of wavetable synthesis in previous sections is the most original definition of the term and (as shown in the reference below) wavetable synthesis is equivalent to additive synthesis in the case that all partials or overtones are harmonic (that is all overtones are at frequencies that are an integer multiple of a fundamental frequency of the tone).

Notes

^ In additive synthesis the evolution of timbre is produced by having a separate time-varying coefficient for each additive component.
^ The loudness contour is not normally produced by the wavetable itself, instead an envelope generator is used.

Wavetable synthesis

Contents